As integrated circuits scale to finer feature sizes, (e.g., with features at or below 45 nm), process variations become increasingly difficult to capture with traditional modeling techniques. Understanding statistical variations has become increasingly important in design efforts to ensure manufacturability and improve parametric yield. Mismatch variation between individual devices is particularly important, so management of mismatch variation impact on circuit performance variation should be made at the circuit design stage.
Variations in circuit performance are often modeled as an additive combination of linear variations. Each variation may typically describe a physical parameter such as an oxide thickness or a threshold voltage. A statistical transistor model may have several mismatch parameters to model its mismatch variations. However, simple linear sensitivity analysis does not provide enough information for designers to fully optimize the design. It provides only sensitivity coefficients for each mismatch parameter, and does not provide information on which particular device in a circuit design has the highest impact on overall circuit performance.
The computational expense of including circuit performance variation analysis in a design cycle can be significant or even prohibitive with current methods. The simulation time of simple OFAT (one-factor-at-a-time) sensitivity analysis generally depends on the number of devices in a circuit multiplied by the number of different mismatch parameters for each. For example, ten mismatch parameters and a thousand devices would require at least 10001 Monte Carlo circuit simulations in current OFAT sensitivity analysis schemes.
Accordingly, the inventors identified a need for identifying important mismatch variation contributions from devices in a circuit design, and with significantly less computational expense than is required for traditional multivariate linear regression.
For example, when the number of sample data points is less than the number of different mismatch parameters, it may not be possible to determine the accuracy of the orthogonal matching pursuit (OMP) model previously described. Further, in some cases, circuit performance variation may be very nonlinearly related to the mismatch parameters. In such cases, the linear mismatch contributions to performance variation will have very low coefficient of determination (R2) values, because linear regression models cannot adequately describe the underlying nonlinear relationships. In other words, the linear mismatch contribution results are not sufficiently representative, because they miss the major variance of the actual output performance.
The inventors have therefore developed a comprehensive methodology to calculate device mismatch variation contributions with a limited number of samples to address these concerns.